Question

If the sum of the first \( n \) terms of an arithmetic progression (AP) is given by \( S_n = 3n^2 + 2n \), find the 4th term of the AP.

• A. 20
• B. 18
• C. 15
• D. 12

Hint:

To find the nth term in an AP, use the formula \( T_n = S_n - S_{n-1} \), where \( S_n \) is the sum of the first \( n \) terms.

Answer 1

The Correct Option is A

The sum of the first \( n \) terms of an AP is given by \( S_n = 3n^2 + 2n \). The nth term \( T_n \) of an AP is given by: \[ T_n = S_n - S_{n-1} \] To find the 4th term, we calculate \( T_4 \): \[ T_4 = S_4 - S_3 \] Now, calculate \( S_4 \) and \( S_3 \): \[ S_4 = 3(4)^2 + 2(4) = 3(16) + 8 = 48 + 8 = 56 \] \[ S_3 = 3(3)^2 + 2(3) = 3(9) + 6 = 27 + 6 = 33 \] Thus: \[ T_4 = 56 - 33 = 23 \] Therefore, the 4th term of the AP is 23, corresponding to option (1).